> Let A, B be the centers of two circles with radius > r1, r2 respectively, where r1-r2 is very small. > Construct the exterior tangent to the given circles. > > In this puzzle is sought a practical construction on an A4 sheet of paper that avoids entirely the use of r1-r2.
Let AA0 be the radius of (A,r1) perpendicular to line AB Let BB0 be the radius of (B,r2) perpendicular to line AB From A drop perp AA1 to line A0B0 From B drop perp BB1 to line A0B0 Produce AA1 to meet circle(A,r1) in A12 Produce BB1 to meet circle(B,r2) in B12
Line A12B12 is a close approx to the required tangent.
A second iteration, by dropping perps from A and B to line A12B12 and extending these to A22B22 will be only marginally more accurate for the tangent line, but it will give a slight improvement of the location of the points of tangency.